How can I transform one end of a cylindrical extrusion to create a cone or needle-like structure?
You are either in Object Mode or have the whole mesh selected.

Make sure that you are in Edit Mode (Tab). In the header of the 3D View:



Then press A repeatedly until nothing is selected. Then use border select (B) for example to select the right most vertices:



Then scale them down. It might be that you have to change your pivot point to Median Point.
Again in the 3D View header:



You also have to make sure that proportional editing is off (O) (header again).